Cross-media colour gamut mapping model for the preservation of visual differentials in layer-tinted maps

Aiming at solving the colour union, variation and loss problems during cross-media reproduction in the layer-tinted map, this study proposes a colour gamut mapping model for the preservation of visual differentials in layer-tinted maps. First, many layer-tinted maps are collected for analysis and the colouring rules are concluded. Then, the dominant and non-dominant colours are extracted based on the colour gamut characteristics of the maps. For the mapping of dominant colours, the corresponding Munsell’s three colour dimensions are calculated by establishing the transformational relation between CIELAB colour space and Munsell’s colour system and then the colour gamut mapping of dominant colours is achieved in the Munsell’s colour order system. On the other hand, the mapping of non-dominant colours is achieved by hue-angle preserving minimum ΔE clipping. The experimental results indicate that compared with the four colour gamut mapping methods recommended by the International Color Consortium, the proposed algorithm in this study can more easily distinguish the hierarchical information in the maps and perfectly remain the visual differentials among the layered colours.


Introduction
As a kind of thematic maps, layer-tinted maps are made by filling the regions of contour lines at different elevations using the different grades of colours with continuously varying hue, saturation and lightness.Owing to certain visual differentials among these different grades of colours, the spatial distributions of various elements on the maps appear to be more visual and the maps are more artistic [1].With the advent of multimedia technology, the loading equipment of maps is no longer limited to paper and now includes computer screen, handheld device etc.However, the device-dependence colours may bring a series of problems during the cross-media reproduction of layer-tinted maps such as colour union, variation and loss, leading to the losses of original visual differentials and even the transfer of wrong geographic information [2].
Colour gamut mapping techniques are generally used for solving the colour inconsistency induced by the difference between source gamut and target gamut [3].The common colour gamut mapping methods fall into two categories, i.e. the colour management method irrelevant to the image contents which was proposed by the International Color Consortium (ICC) and the colour gamut mapping algorithms correlated with the image contents.As for the device-to-device mapping, ICC proposes that four different kinds of rendering intents can be achieved with the use of CIELAB colour space as the profile connection space in mapping [4].However, the colour gamut characteristics are not taken into account in this colour management method.In addition, the CIELAB colour space shows a poor uniformity of hue angle in blue regions, which will cause great adverse effects on the transmission of blue-based oceanic maps [5].As to the colour gamut mapping correlated with image contents, Golan and Hel-Or [6] selected the colour gamut mapping algorithm in accordance with image features, and thus the mapping of images can be self-adaptive to the algorithm.On the basis of the principle of Retinex Theory, McCann et al. put forward a self-adaptive mapping method for maintaining the spatial gradient of images [7].Bala et al. extract the image's high-frequency and low-frequency channels using spatial filtering method, based on which different mapping methods are adopted to maintain the lightness gradient of images [8].However, layer-tinted map is a kind of special thematic map, which differs greatly from normal images in colouring rule.Moreover, the extraction difficulty is also increased on account of the addition of other attributes such as image frequency and gradient [9].
To resolve the defect that the colour gamut characteristics are not considered in the existing map colour management system, this paper proposes a novel colour gamut mapping algorithm for layertinted maps.First, the colouring rules are analysed and concluded through collecting several layer-tinted maps.Then, the dominant and non-dominant colours of the maps are extracted based on the gamut characteristics of various colours.Finally, the corresponding Munsell's three colour dimensions of the dominant colours are calculated by establishing the transformational relation between CIELAB colour space and Munsell's colour system, while the mapping of non-dominant colours are achieved using the hue-angle preserving minimum ΔE clipping.As demonstrated by the experimental results, the visual differentials among the layered colours can be well preserved in the layer-tinted maps using the proposed method, so that the readers can quickly distinguish the hierarchical information in the maps.

Analysis of the colouring rules in layer-tinted maps
A typical layer-tinted map is shown in Fig. 1a, which presents the proportion of China's employment population.It can be observed that this layer-tinted map consists of dominant and non-dominant colours.As shown in Fig. 1b, the dominant colours correspond to a series of layered colours with continuous changes, which are used for describing the specific hierarchical information in the map; the non-dominant colours are generally applied to describe the auxiliary elements in the map such as rivers, lakes and boundaries, which differ greatly from the dominant colours in visual sensation.
Total 3 Divide-and-conquer mapping scheme for dominant and non-dominant colours According to the analysis results, the dominant colours in the layer-tinted map show more concentrated distributions than the non-dominant colours and exhibit the visual differentials with continuous variations.There is no obvious correlation between the dominant and non-dominant colours.The dominant colours play a role in transferring hierarchical information of the map, and thus the key of mapping is to preserve the visual differentials among different grades of colours as much as possible.If the CIELAB colour space is adopted as the profile connection space in mapping, it becomes harder to ensure that the dominant colours still have enough visual differentials after the mapping due to the poor uniformity of hue angle in CIELAB colour space, and then the geographic information included in the map may be lost.
Munsell colour system is a colour classification and calibration system based on human vision matching experiments, in which the colours are described by the values of hue, lightness and chroma (H, V and C ).This system has a favourable visual uniformity.When the sum of colour scale difference (ΔV, ΔH and ΔC) between two Munsell colours exceeds one unit of Munsell colour scale, these two colours can be distinguished by human eyes [10].In this paper, the Munsell colour system is introduced in the cross-media reproduction of maps by calculating the corresponding Munsell colour scales of the dominant colours.Moreover, the visual differentials among the dominant colours have remained by setting limitations on the Munsell colour scale differences between different dominant colours after mapping.Currently, the common transformation algorithms between the CIELAB colour space and Munsell colour system include vector algebra method, intercept and slope interpolation method, linear interpolation method [11] etc. In view of calculation accuracy and time complexity, the linear interpolation method specified in [11] is adopted in the present paper for the conversion of dominant colours between two colour systems.
More attention should be paid on the accuracy of colour transmission during the cross-media reproduction of non-dominant colours, which is different from the dominant colours.Therefore, a divide-and-conquer mapping scheme is proposed for dominant and non-dominant colours proposed in this paper, and the specific calculation flow of the algorithm is shown in Fig. 3. Next, the colour with the largest pixel proportion is selected from the map database A and denoted as Colour-1.On the basis of the colouring rule of layer-tinted maps, Colour-1 is a dominant colour.Finally, the CIELAB hue-angle differences between Colour-1 and all other colours in the map database A are calculated.If the hue-angle difference is within the range of 0°and 30°and the pixel proportion is larger than 10%, the colour can be denoted as a dominant colour; otherwise, the colour will be denoted as a non-dominant colour.For the dominant colours stored in the map database A, the following steps ( 4)-( 7) will be executed; for the non-dominant colours, the following step (8) will be implemented.(iv) All dominant colours stored in the map database A are extracted, and the corresponding Munsell three colour scales are calculated using the method described in [11].The maximum and minimum Munsell hue values of the dominant colours are denoted as (H max , H min ), and then for any layertinted map, the Munsell lightness variation range can be calculated as below where V max and V min denote the maximum and minimum Munsell hue values of each dominant colour, respectively, and k denotes the number of dominant colours in the map.The Munsell colour scale difference between each dominant colour and all colours stored in the colour gamut database B can be calculated as below

Experimental verification
The proportion map of agricultural population is used for testing the feasibility of the algorithm proposed in this paper, as shown in Fig. 4a.During the test, the source device (LE1901w1, HP Compaq) and the target device (T43, IBM Thinkpad) are calibrated using the software and hardware equipment (X-Rite Eye-One), and the ICC profile files of the devices can be obtained.Fig. 4b shows the colour gamut ranges of two display devices, in which the colour gamut of source device is displayed in a wireframe mode, while that of the target device is displayed in an entity mode.It can be observed that the source device has a greater colour gamut than the target device, and most of colours in the map have the colour gamut between that of the source and target devices.
The experiment is then conducted on the already calibrated device.By means of the colour setting function in Photoshop image processing software, the ICC profile files of the source and target devices are loaded on the test map.The mapping of the test map is achieved using the algorithm as described in Section 3, and this process is performed in MATLAB.Fig. 5 displays the mapped results using different mapping methods.
As shown in Fig. 5, different degrees of colour union can be observed in the test maps treated according to four mapping intents in the ICC colour management system.By comparison, the hierarchical information of the original map can be well preserved using the proposed algorithm in this paper.To further verify the better mapping results, the differentials among dominant colours in the above-described five mapping maps are calculated using (3) and the statistical results are listed in Table 1.
The items 1-7 in Table 1 denote dominant colours at seven levels in the test map from light to dark.It can be observed that when using the four mapping algorithms recommended by ICC, the visual differentials among different grades of dominant colours are reduced greatly.However, using the proposed mapping algorithm in this paper, the visual differentials in the mapping map are almost unchanged compared with those in the original map.The analysis results indicate that when using the latter mapping algorithm, not only the hierarchical information in the map can be easily distinguished, but also the mapping image is closer to the original image in terms of visual effect.

Conclusion
On the basis of the analyses on the colouring rule of layer-tinted map, a colour gamut mapping algorithm in which the dominant and non-dominant colours are treated separately is proposed in this paper.For dominant colours, the corresponding Munsell three colour dimensions are calculated by establishing the transformational relation between the CIELAB colour space and Munsell colour system, and then the colour gamut mapping is conducted in the Munsell colour order system; for non-dominant colours, the mapping is achieved using the hue-angle preserving minimum ΔE clipping.The experimental results indicate using the proposed algorithm in this paper, the colour union occurred in the mapping of layered colours can be effectively solved.This algorithm can be widely applied in the cross-media reproduction of various layer-tinted maps such as oceanographic map and classified statistical diagram.

Acknowledgment
This work was supported by the National Natural Science Foundation of China (Grant No. 41271446).
298 layer-tinted maps, selected from The Atlas of Population, Environment and Sustainable Development of China, The Atlas of Population and Environmental Change of China and American ColorBrewer atlas, are used in the present study for colour analyses.The colouring characteristics of layer-tinted maps can be concluded as below: (i) The layer-tinted maps mainly represent the continuous hierarchical information by varying the lightness and saturation of dominant colours, in which the light colours generally represent the low-grade values and the dark colours represent the high-grade values.The lightness of dominant colours decreases gradually in an ascending order of grade, and the dominant colours at different grades decrease monotonically along the L*-axis in the CIELAB colour space.(ii) As shown in Fig. 2a, the dominant colours of the layer-tinted map exhibit slight changes in hue, whose hue-angle differences are generally within a certain range (0-30°) in a-b coordinate system of the CIELAB colour space.Such a design can guarantee the integral continuity of various dominant colours in visual sense.On the other hand, as shown in Fig. 2b, the hue-angle differences of the non-dominant colours are scattered in the CIELAB colour space.(iii) In a layer-tinted map, the pixel proportions of various dominant colours in the whole map (i.e. the ratio of the pixel number of layered colour to the total pixel numbers of the map) generally exceed 10%, whereas the pixel proportions of the nondominant colours in the whole map are below 10%.

Fig. 1
Fig. 1 Example of layer-tinted map a Proportion of China's employment population b Combination of common dominant colours

Fig. 3
Fig. 3 Optimal mapping scheme for dominant and non-dominant colours of the layer-coloured map

P 1
2) where (V n , H n , C n ) and (V M , H M , C M ) denote the Munsell three colour scale values of the colours stored in the colour gamut database B and the dominant colours.Considering the changes of adjacent hue and chroma at the intervals of 2.5 and 2 in the Munsell colour system, the calculation results of Munsell hue and chroma differences from (2) are normalised.(v) For the specific dominant colours to be mapped (marked as M), all the colours with the Munsell hue values ranging between H min and H max and the Munsell lightness values ranging between (V M − 1/2V range ) and (V M + 1/2V range ) (marked as C) are selected from the colour gamut database B. (vi) Selected from all colours with the ΔMunsell >1 in the colour set C, a special colour with the minimum ΔMunsell value is marked as the Point E. The Munsell hue and lightness values of Point E can meet the colouring requirement of dominant colours; there exist sufficient visual differentials between Point E and the other dominant colours except the dominant colour M. Then the CIELAB colour value of Point E is taken as the colour value of the dominant colour M after mapping.(vii) The colour gamut mapping of the rest of dominant colours is conducted by repeating the steps 5 and 6 described above.(viii) For a non-dominant colour to be mapped (marked as the Point P), the CIELAB colour difference ΔE between Point P and all colours in the colour gamut database B is calculated, and the CIELAB value of the target colour with minimum ΔE is taken as the colour value of Point P after mapping.Accordingly, the optimal mapping of non-dominant colours can be achieved.The CIELAB colour difference ΔE can be calculated as below DE = L * n − L * n *, a n *, b n *) and (L P *, a P *, b P *) denote the CIELAB

Fig. 4 Fig. 5
Fig. 4 Experimental map and colour gamut of the device used in experiment a Proportion of agricultural population b Colour gamut of the source and target devices

Table 1
Calculation results of the visual differentials